The first practice question is a simple problem (finding a labeled coordinate on a number line based on the surrounding numbers). The second question is a little trickier (finding the coordinate of a point on the line based on its distance from other points).

## Practice questions

- The distance from one labeled coordinate to the next on the number line is the same in every case. What is the value of
*y*?**A.**17.5**B.**18.5**C.**17**D.**16**E.**18 - For this number line, the distance from
*P*to*Q*is half the distance from*Q*to*R,*and that distance is half the distance from*R*to*S.*The coordinate of*P*is 4, and the coordinate of*R*is 10. What is the coordinate of*S?***A.**18**B.**16**C.**20**D.**24**E.**14

## Answers and explanations

- The correct answer is Choice
**(E).**The distance is the same from one labeled coordinate to the next in every case. Some of the labels indicate that each coordinate is 3 units away from the adjacent ones. The number that's 3 more than 15 and 3 less than 21 is 18. - The correct answer is Choice
**(A).**You can figure out the distance from*P*to*S*if you determine the distance from*P*to*Q*, because the distance from*P*to*S*is that distance, plus twice that distance, plus twice that.The distance from

*P*to*R*is 6 because 10 – 4 = 6.*Q*is in a position in which its distance from*P*is half its distance from*R*. The sum of those distances is 6. Therefore, the distance from*P*to*Q*is a number that can be added to twice itself to get 6. That number is 2.2 + 2(2) = 6

You could use algebra to determine that, but it's not necessary. Because the distance from

*P*to*Q*is 2, you know that the distance from*Q*to*R*is 4 and that the distance from*R*to*S*is 8. The coordinate of*P*is 4, so the coordinate of*S*is 4 + 2 + 4 + 8, or 18.